Test Booklet Code JEE-MAIN 2013 P - Vidyalankar

1 (Pg. 1) . JEE-MAIN 2013 . PAPER - 1 : PHYSICS, CHEMISTRY & MATHEMATICS Do not open this Test Booklet until you are asked to do so. Read carefully the Instructions on the Back Cover of this Test Booklet . Important Instructions : 1. Immediately fill in the particulars on this page of the Test Booklet with Blue/Black Ball Point Pen. Use of pencil is strictly prohibited. 2. The Answer Sheet is kept inside this Test Booklet . When you are directed to open the Test Booklet , take out the Answer Sheet and fill in the particulars carefully. 3. The test is of 3 hours duration. 4. The Test Booklet consists of 90 questions. The maximum marks are 360. 5. There are three parts in the question paper A, B, C consisting of, Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage.

2 Each question is allotted 4 (four) marks for each correct response. 6. Candidates will be awarded marks as stated above in instruction No. 5 for correct response of each question. 1/4 (one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet. 7. There is only one correct response for each question. Filling up more than one response in any question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 6 above. 8. Use Blue/Black Ball Point Pen only for writting particulars/ marking responses on Side 1 and Side 2 of the Answer Sheet.

3 Use of pencil is strictly prohibited. 9. No candidates is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc., except the Admit Card inside the examination hall/room. 10. Rough work is to be done on the space provided for this purpose in the Test Booklet only. This space is given at the bottom of each page and in 3 pages (Pages 21 23) at the end of the Booklet . 11. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room / Hall. However, the candidates are allowed to take away this Test Booklet with them. 12. The code for this Booklet is P. Make sure that the code printed on Side 2 of the Answer Sheet is the same as that on this Booklet . In case of discrepancy, the candidate should immediately report the matter to the invigilator for replacement of both the Test Booklet and the Answer Sheet.

4 13. Do not fold or make any stray marks on the Answer Sheet. Name of the Candidate (in Capital letters) : _____ Roll Number : in figures : in words _____ Examination Centre Number : Name of Examination Centre (in Capital letters) : _____ Candidate s Signature : _____ Invigilator s Signature : _____ Test Booklet CodePJEE- main 2013 : Paper and Solution (2) (Pg. 2) READ THE FOLLOWING INSTRUCTIONS CAREFULLY : 1. The candidates should fill in the required particulars on the Test Booklet and Answer Sheet (Side-1) with Blue/Black Ball Point Pen. 2. For writing/marking particulars on Side-2 of the Answer Sheet, use Blue/Black Ball Point Pen only.

5 3. The candidates should not write their Roll Numbers anywhere else (except in the specified space) on the Test Booklet /Answer Sheet. 4. Out of the four options given for each question, only one option is the correct answer. 5. For each incorrect response, one-fourth ( ) of the total marks allotted to the question would be deducted from the total score. No deduction from the total score, however, will be made if no response is indicated for an item in the Answer Sheet. 6. Handle the Test Booklet and Answer Sheet with care, as under no circumstances (except for discrepancy in Test Booklet code and Answer Sheet code ), will another set be provided. 7. The candidates are not allowed to do any rough work or writing work on the Answer Sheet.

6 All calculations/writing work are to be done in the space provided for this purpose in the Test Booklet itself, marked Space for Rough Work . This space is given at the bottom of each page and in 3 pages (Pages 21 23) at the end of the Booklet . 8. On completion of the test, the candidates must hand over the Answer Sheet to the Invigilator on duty in the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them. 9. Each candidate must show on demand his/her Admit Card to the Invigilator. 10. No candidate, without special permission of the Superintendent or Invigilator, should leave his/her seat. 11. The candidates should not leave the Examination Hall without handing over their Answer Sheet to the Invigilator on duty and sign the Attendance Sheet again.

7 Cases where a candidate has not signed the Attendance Sheet a second time will be deemed not to have handed over the Answer Sheet and dealt with as an unfair means case. The candidates are also required to put their left hand THUMB impression in the space provided in the Attendance Sheet. 12. Use of Electronic/Manual Calculator and any Electronic Item like mobile phone, pager etc. is prohibited. 13. The candidates are governed by all Rules and Regulations of the JAB/Board with regard to their conduct in the Examination Hall. All cases of unfair means will be dealt with as per Rules and Regulations of the JAB/Board. 14. No part of the Test Booklet and Answer Sheet shall be detached under any circumstances. 15. Candidates are not allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, electronic device or any other material except the Admit Card inside the examination hall/room.

8 (3) Vidyalankar : JEE-MAIN 2013 : Paper and Solution (Pg. 3) .Questions and Solutions. PART- A : PHYSICS 1. A uniform cylinder of length L and mass M having cross - sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density at equilibrium position. The extension x0 of the spring when it is in equilibrium is : (1) Mgk (2) MgLA1kM (3) MgLA1k2M (4) MgLA1kM + (Here, k is spring constant) 1. (3) 0 LAKxgmg2 + = x0 = MgLA1k2M 2. A metallic rod of length A is tied to a string of length 2A and made to rotate with angular speed on a horizontal table with one end of the string fixed. If there is a vertical magnetic field B in the region, the induced across the ends of the rod is : (1) 22B2 A (2) 23B2 A (3) 24B2 A (4) 25B2 A 2.

9 (4) V = ()32vBdx Bdx = AAJJGGGA V = 25B2 A 3. This question has statement I and Statement II. Of the four choice given after the statements, choose the one that best describes the two statements. Statement I : A Point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as 21mfmvthenf2Mm = + . Statement II : Maximum energy loss occurs when the particles get stuck together as a result of the collision. (1) Statement - I is true, Statement - II is true, statement - II is a correct explanation of Statement - I (2) Statement - I is true, Statement - II is true, statement - II is not a correct explanation of Statement I (3) Statement - I is true, Statement - II is false (4) Statement I is false, Statement II is true A2 AxV ga JEE-MAIN 2013 : Paper and Solution (4) (Pg.)

10 4) 3. (4) Maximum energy loss when inelastic collision takes place mv = (m + M) v v = mvmM+ 2i1kmv2= 2222f211mv1mk(mM)v'(mM)mv222Mm(m M) =+ =+= ++ Loss of energy = 22if1mM1kkmv1mv2 MmMm2 = = ++ 4. Let [ 0] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = Time and A = electric current, then : (1) [ 0] = [M 1 L 3 T2 A] (2) [ 0] = [M 1 L 3 T4 A2] (3) [ 0] = [M 1 L2 T 1 A 2] (4) [ 0] = [M 1 L2 T 1 A] 4. (2) []2220222 CATNmMLT L == []13420 MLTA = 5. A Projectile is given an initial velocity of (i 2 j) m/s,+ where iis along the ground and j is along the vertical. If g = 10 m/s2, the equation of its trajectory is : (1) y = x 5x2 (2) y = 2x 5x2 (3) 4y = 2x 5x2 (4) 4y = 2x 25x2 5.